The OEM wiring gets power for the relay from the headlights...so they have to be getting power to power the fogs...and the low beams at that, so they go off if you hit the hi-beams as well.
To get independant operation, re-wire it so you get power to the relay from the fuse box directly...so its always hot, and or from a hot source with the ignition on if you want them to go off when you trun the engine off, etc.
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- TJ
2001 Xterra '03 VG33, SE 5 spd, 305/70/16's, Revolvers, UBSkidderz, Doubled AAL's, 3"SL/2"BL, winch/bumpers, skids, sliders, OBA, Snorkel, pine stripes....
Friends don't let friends drive stock.
http://www.gifsoup.com/view/501230/tj-tackling-crawlers-ridge-o.gif